We discuss a number of distance functions encountered in the theory of computation, including metrics, ultra-metrics, quasi-metrics, generalized ultra-metrics, partial metrics, d-ultra-metrics and generalized metrics. We consider their properties, associated fixed-point theorems and some general applications they have within the theory of computation. We consider in detail the applications of generalized distance functions in giving a uniform treatment of several important semantics for logic programs, including acceptable programs and natural generalizations of them, and also the supported model and the stable model in the context of locally stratified extended disjunctive logic programs and databases.

10adenotational semantics10afixed-point theorems10ageneralized distance functions10aLogic Programming10astable model10asupported model10atopology10aultra-metrics1 aSeda, Anthony, K.1 aHitzler, Pascal uhttp://dx.doi.org/10.1093/comjnl/bxm10801540nas a2200193 4500008004100000245003000041210002800071300001200099490000600111520103000117653002401147653002101171653002901192653002101221653001701242100002001259700002401279856004301303 2010 eng d00aA Reasonable Semantic Web0 aReasonable Semantic Web a39–440 v13 aThe realization of Semantic Web reasoning is central to substantiating the Semantic Web vision. However, current mainstream research on this topic faces serious challenges, which forces us to question established lines of research and to rethink the underlying approaches. We argue that reasoning for the Semantic Web should be understood as "shared inference," which is not necessarily based on deductive methods. Model-theoretic semantics (and sound and complete reasoning based on it) functions as a gold standard, but applications dealing with large-scale and noisy data usually cannot afford the required runtimes. Approximate methods, including deductive ones, but also approaches based on entirely different methods like machine learning or natureinspired computing need to be investigated, while quality assurance needs to be done in terms of precision and recall values (as in information retrieval) and not necessarily in terms of soundness and completeness of the underlying algorithms.

10aAutomated Reasoning10aFormal Semantics10aKnowledge representation10aLinked Open Data10aSemantic Web1 aHitzler, Pascal1 avan Harmelen, Frank uhttp://dx.doi.org/10.3233/SW-2010-0010